A318048 Size of the span of the unlabeled rooted tree with Matula-Goebel number n.

1, 2, 3, 2, 4, 4, 4, 2, 6, 6, 5, 4, 6, 3, 9, 2, 6, 6, 4, 6, 6, 8, 10, 4, 12, 6, 10, 4, 9, 9, 6, 2, 12, 6, 9, 6, 6, 4, 9, 6, 9, 7, 6, 8, 15, 10, 15, 4, 5, 12, 9, 7, 4, 10, 16, 4, 7, 9, 8, 9, 10, 10, 11, 2, 13, 12, 6, 7, 14, 10, 9, 6, 10, 7, 21, 3, 12, 10, 12, 6

Offset: 1

Author

Gus Wiseman, Aug 13 2018

Keywords

• nonn

Comments

The span of a tree is defined to be the set of possible terminal subtrees of initial subtrees, or, which is the same, the set of possible initial subtrees of terminal subtrees.

Examples

			42 is the Matula-Goebel number of (o(o)(oo)), which has span {o, (o), (oo), (ooo), (oo(oo)), (o(o)o), (o(o)(oo))}, so a(42) = 7.
		

Links

• Index entries for sequences related to Matula-Goebel numbers

Crossrefs

Cf. A000081, A007097, A007853, A049076, A061773, A061775, A109082, A109129, A206491, A317713, A318046.

Programs

Mathematica

ext[c_,{}]:=c;ext[c_,s:{}]:=Extract[c,s];rpp[c_,v_,{}]:=v;rpp[c_,v_,s:{}]:=ReplacePart[c,v,s];
RLO[ear_,rue:{}]:=Union@@(Function[x,rpp[ear,x,#2]]/@ReplaceList[ext[ear,#2],#1]&@@@Select[Tuples[{rue,Position[ear,_]}],MatchQ[ext[ear,#[[2]]],#[[1,1]]]&]);
RL[ear_,rue:{}]:=FixedPoint[Function[keeps,Union[keeps,Join@@(RLO[#,rue]&/@keeps)]],{ear}];
primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
MGTree[n_]:=If[n==1,{},MGTree/@primeMS[n]];
Table[Length[Union[Cases[RL[MGTree[n],{List[__List]:>List[]}],_List,{1,Infinity}]]],{n,100}]